Sequence-Based Prediction of Protein Phase Separation: The Role of Beta-Pairing Propensity.

The formation of droplets of bio-molecular condensates through liquid-liquid phase separation (LLPS) of their component proteins is a key factor in the maintenance of cellular homeostasis. Different protein properties were shown to be important in LLPS onset, making it possible to develop predictors, which try to discriminate a positive set of proteins involved in LLPS against a negative set of proteins not involved in LLPS. On the other hand, the redundancy and multivalency of the interactions driving LLPS led to the suggestion that the large conformational entropy associated with non specific side-chain interactions is also a key factor in LLPS. In this work we build a LLPS predictor which combines the ability to form pi-pi interactions, with an unrelated feature, the propensity to stabilize the ß-pairing interaction mode. The cross-ß structure is formed in the amyloid aggregates, which are involved in degenerative diseases and may be the final thermodynamically stable state of protein condensates. Our results show that the combination of pi-pi and ß-pairing propensity yields an improved performance. They also suggest that protein sequences are more likely to be involved in phase separation if the main chain conformational entropy of the ß-pairing maintained droplet state is increased. This would stabilize the droplet state against the more ordered amyloid state. Interestingly, the entropic stabilization of the droplet state appears to proceed according to different mechanisms, depending on the fraction of "droplet-driving" proteins present in the positive set.

Analysis of emergent patterns in crossing flows of pedestrians reveals an invariant of 'stripe' formation in human data.

When two streams of pedestrians cross at an angle, striped patterns spontaneously emerge as a result of local pedestrian interactions. This clear case of self-organized pattern formation remains to be elucidated. In counterflows, with a crossing angle of 180°, alternating lanes of traffic are commonly observed moving in opposite directions, whereas in crossing flows at an angle of 90°, diagonal stripes have been reported. Naka (1977) hypothesized that stripe orientation is perpendicular to the bisector of the crossing angle. However, studies of crossing flows at acute and obtuse angles remain underdeveloped. We tested the bisector hypothesis in experiments on small groups (18-19 participants each) crossing at seven angles (30° intervals), and analyzed the geometric properties of stripes. We present two novel computational methods for analyzing striped patterns in pedestrian data: (i) an edge-cutting algorithm, which detects the dynamic formation of stripes and allows us to measure local properties of individual stripes; and (ii) a pattern-matching technique, based on the Gabor function, which allows us to estimate global properties (orientation and wavelength) of the striped pattern at a time T. We find an invariant property: stripes in the two groups are parallel and perpendicular to the bisector at all crossing angles. In contrast, other properties depend on the crossing angle: stripe spacing (wavelength), stripe size (number of pedestrians per stripe), and crossing time all decrease as the crossing angle increases from 30° to 180°, whereas the number of stripes increases with crossing angle. We also observe that the width of individual stripes is dynamically squeezed as the two groups cross each other. The findings thus support the bisector hypothesis at a wide range of crossing angles, although the theoretical reasons for this invariant remain unclear. The present results provide empirical constraints on theoretical studies and computational models of crossing flows.

Effect of bias in a reaction-diffusion system in two dimensions.

We consider a single species reaction diffusion system on a two-dimensional lattice where the particles A are biased to move towards their nearest neighbors and annihilate as they meet. Allowing the bias to take both negative and positive values parametrically, any nonzero bias is seen to drastically affect the behavior of the system compared to the unbiased (simple diffusive) case. For positive bias, a finite number of dimers, which are isolated pairs of particles occurring as nearest neighbors, exist while for negative bias, a finite density of particles survives. Both the quantities vanish in a power-law manner close to the diffusive limit with different exponents. The appearance of dimers is exclusively due to the parallel updating scheme used in the simulation. The results indicate the presence of a continuous phase transition at the diffusive point. In addition, a discontinuity is observed at the fully positive bias limit. The persistence behavior is also analysed for the system.

Virtual walks in spin space: A study in a family of two-parameter models.

We investigate the dynamics of classical spins mapped as walkers in a virtual "spin" space using a generalized two-parameter family of spin models characterized by parameters y and z [de Oliveira et al., J. Phys. A 26, 2317 (1993)JPHAC50305-447010.1088/0305-4470/26/10/006]. The behavior of S(x,t), the probability that the walker is at position x at time t, is studied in detail. In general S(x,t)∼t^{-α}f(x/t^{α}) with α≃1 or 0.5 at large times depending on the parameters. In particular, S(x,t) for the point y=1,z=0.5 corresponding to the Voter model shows a crossover in time; associated with this crossover, two timescales can be defined which vary with the system size L as L^{2}logL. We also show that as the Voter model point is approached from the disordered regions along different directions, the width of the Gaussian distribution S(x,t) diverges in a power law manner with different exponents. For the majority Voter case, the results indicate that the the virtual walk can detect the phase transition perhaps more efficiently compared to other nonequilibrium methods.

Zero-temperature coarsening in the Ising model with asymmetric second-neighbor interactions in two dimensions.

We consider the zero-temperature coarsening in the Ising model in two dimensions where the spins interact within the Moore neighborhood. The Hamiltonian is given by H=-∑_{〈i,j〉}S_{i}S_{j}-κ∑_{〈i,j^{'}〉}S_{i}S_{j^{'}}, where the two terms are for the first neighbors and second neighbors, respectively, and κ≥0. The freezing phenomenon, already noted in two dimensions for κ=0, is seen to be present for any κ. However, the frozen states show more complicated structure as κ is increased; e.g., local antiferromagnetic motifs can exist for κ>2. Finite-sized systems also show the existence of an isoenergetic active phase for κ>2, which vanishes in the thermodynamic limit. The persistence probability shows universal behavior for κ>0; however, it is clearly different from the κ=0 results when a nonhomogeneous initial condition is considered. Exit probability shows universal behavior for all κ≥0. The results are compared with other models in two dimensions having interactions beyond the first neighbor.

Minority-spin dynamics in the nonhomogeneous Ising model: Diverging time scales and exponents.

We investigate the dynamical behavior of the Ising model under a zero-temperature quench with the initial fraction of up spins 0≤x≤1. In one dimension, the known results for persistence probability are verified; it shows algebraic decay for both up and down spins asymptotically with different exponents. It is found that the conventional finite-size scaling is valid here. In two dimensions, however, the persistence probabilities are no longer algebraic; in particular for x≤0.5, persistence for the up (minority) spins shows the behavior P_{min}(t)∼t^{-γ}exp[-(t/τ)^{δ}] with time t, while for the down (majority) spins, P_{maj}(t) approaches a finite value. We find that the timescale τ diverges as (x_{c}-x)^{-λ}, where x_{c}=0.5 and λ≃2.31. The exponent γ varies as θ_{2d}+c_{0}(x_{c}-x)^{ß} where θ_{2d}≃0.215 is very close to the persistence exponent in two dimensions; ß≃1. The results in two dimensions can be understood qualitatively by studying the exit probability, which for different system size is found to have the form E(x)=f[(x-x_{c}/x_{c})L^{1/ν}], with ν≈1.47. This result suggests that τ∼L^{z[over ̃]}, where z[over ̃]=λ/ν=1.57±0.11 is an exponent not explored earlier.